Due to the sporadic characteristic of IoT data traffic, active device detection is a typical sparse signal recovery problem. Specifically, active device detection is equivalent to the recovery of the sparse device state matrix from the noisy measurements. Therefore, many works attempt to address the problem of active device detection by using compressed sensing (CS) approaches [1]}. For instance, the authors in [2]} proposed a generalized turbo signal recovery algorithm which was capable of achieving good performance and strong robustness in solving the active device detection problem with a mixed analog-to-digital converter (ADC) architecture. By exploiting both the active device sparsity and the chunk sparsity feature of the channel matrix, the authors in [3]} proposed a modified Bayesian CS algorithm, which can further improve the detection performance. If channel information is available, the accuracy of active device detection can be significantly increased. Motivated by that, the authors in [4]} and [5]} proposed an approximate message passing (AMP) algorithm for active device detection by making use of the statistical information of wireless channels. It was proved that if the number of BS antennas was sufficiently large, the detection error asymptotically approached zero in the case that the elements of pilot sequences were independent and identically distributed (i.i.d.) Gaussian random variables with zero mean. To provide more pilot sequences with a given length, pilot sequences have to be non-i.i.d. For improving the estimation performance in the case of non-i.i.d. pilot sequences, a vector AMP (VAMP) algorithm was proposed in [6]} by introducing a linear minimum mean square error (LMMSE) estimator into AMP. Note that the aforementioned approaches in [2]}-[6]} performed active device detection based on the instantaneous received signals, which requires exceedingly long pilot sequences in the scenario of massive access. To tackle this problem, the covariance-based algorithms were proposed in [9]}-[10]} to improve the performance of device activity detection. In specific, [9]} formulated
device activity detection as an maximum likelihood (ML) estimation problem, in which the received signals at multiple antennas affected the detection results via their empirical covariance matrix. Then, [12]} proposed a joint device activity and data detection scheme based on the covariance matrix of the received signals, and analyzed the distribution of the estimation error in the massive MIMO regime. In fact, the covariance-based algorithm can outperform the AMP algorithm with the same length of pilot sequences. However, such a superior system performance comes from the expense of the use of a relatively large number of BS antennas. Although the algorithms in [2]}-[14]} can achieve good detection performance by exploiting the sparsity structure of the device state matrix, they impose high computational complexity due to large-dimensional matrix operators caused by the large-scale antenna array and the massive number of IoT devices [15]}. More importantly, these algorithms require long pilot sequences, which cannot satisfy the requirement of short-packet communications in the context of small IoT payload. As a result, active device detection in 6G wireless networks has emerged as a challenging problem due to a large number of devices and the limited radio resources in wireless networks [16]}, [17]}.
